Question: Simplify the following expression: $z = \dfrac{x^2 - 2x - 8}{x + 2} $
First factor the polynomial in the numerator. $ x^2 - 2x - 8 = (x + 2)(x - 4) $ So we can rewrite the expression as: $z = \dfrac{(x + 2)(x - 4)}{x + 2} $ We can divide the numerator and denominator by $(x + 2)$ on condition that $x \neq -2$ Therefore $z = x - 4; x \neq -2$